Acta mathematica scientia, Series B >
POSITIVE SOLUTIONS TO THE p-LAPLACIAN WITH SINGULAR WEIGHTS
Received date: 2010-09-26
Online published: 2012-05-20
Supported by
This work was supported by the National Natural Science Foundation of China 10771032.
By the Mountain Pass Theorem, we study existence and multiplicity of posi-tive solutions of p-laplacian equation of the form −Δpu = λf(x, u), the nonlinearity f(x, u) grows as uσ at infinity with a singular coefficient, where σ∈ (p − 1, p*− 1). To manage the asymptotic behavior of its positive solutions with respect to λ, we establish a new Liouville-type theorem for the p-Laplacian operator.
Key words： p-Laplacian; variational methods; Sobolev-Hardy exponents
WANG Ying , LUO Dang , WANG Ming-Xin . POSITIVE SOLUTIONS TO THE p-LAPLACIAN WITH SINGULAR WEIGHTS[J]. Acta mathematica scientia, Series B, 2012 , 32(3) : 1002 -1020 . DOI: 10.1016/S0252-9602(12)60075-7
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